The call probably got dispatched as a minor mva no fire apparatus needed but when the ambulance got to the scene they realized they needed the extra backs. So yes you are right the engine was there for BLS support. The ems crew was following BMFD's protocol for lift assists where they call for eng 92 or Res 37 depending on what side of the village the call is on. Regarding Archville's district, as far as I know there district covers the extreme southern end of the Sleepy Hollow Country Club (with the district line virtually going through the horse stables). They also cover Sleepy Hollow rd and the extension up until the borders of the Village of Briarcliff and Sleepy Hollow. I don't know if AFD's district includes Phelps are not but they do protect most of Rockfeller Park by the river and the old IBM building which I think is now New York Life. They have a mutual aid agreement with Pocantico Hills for all structure calls. There is an agreement with Briarcliff, where Eng 92 responds as requested by Archville's IC to the scene of MVA's. Since Archville was not dispatched for this mva the IC most likely was the ambulance's crew chief who requested the help for lifting. I also want to point out that the majority, if not all, of Archville's fire district is covered by Briarcliff Ambulance. If I missed anything I'm sure engine 235 or any member of Scarborough Engine Company will correct me. Hope this has been helpful.